Dynamic surface control with a nonlinear disturbance observer for multi-degree of freedom underactuated mechanical systems

Underactuated systems are extensively utilized in practice while attracting a huge deal of attention in theoretical studies. There are few robust control strategies for general underactuated systems because of the variety of their dynamic models. A dynamic surface control strategy with a nonlinear disturbance observer is proposed in this study, to stabilize multi-degree of freedom underactuated systems. In such systems the number of underactuated degrees of freedom is not higher compared to the actuated ones. A disturbance observer is utilized to dispose of the uncertain disturbance and cross terms in dynamic model which may cause failure to the controller. Then, a dynamic surface control strategy is presented which is not sensitive to the diversity of dynamic models. The stability of whole system is proven by Lyapunov-based method. The control law is successfully applied to nonlinear underactuated systems in benchmark cascade form such as two-translational oscillator with rotational actuator, crane, wheeled inverted pendulum. The effectiveness of proposed controllers are illustrated by MATLAB simulation results. Finally, comparative studies are presented to verify the superiority of the proposed method.